Estimates the value of PI (parallel implementation)

my_parallel_pi.py

#coding: utf-8
# Estimates the value of PI
# Based on example described at http://code.google.com/edu/parallel/mapreduce-tutorial.html#Basics
# Author: Marcelo Criscuolo (Jaú), with 
# invaluable contributions from Rafael Giusti (Argentino)

import math
from datetime import datetime
from multiprocessing import Pool, cpu_count

RADIUS = 80000000 # the bigger the number, more precise is the estimation
try:
	PROCESSES = cpu_count() + 1
except:
	PROCESSES = 3

SQ_RADIUS = RADIUS ** 2


def estimate_area(initial_y, final_y):
	x = RADIUS
	y = initial_y
	area_section = 0
	while y < final_y:
	    sq_y = y ** 2
	    while (sq_y + (x ** 2)) > SQ_RADIUS:
		x -= 1
	    area_section += x
	    y += 1
	return area_section


def main():
	t0 = datetime.now()
	pool = Pool(processes=PROCESSES)
	results = []
	begin = 0
	end = 0
	batch_size = RADIUS // (2 * PROCESSES) # 2 batches per process
	while end < RADIUS:
		begin = end
		end += batch_size
		if end > RADIUS:
			end = RADIUS
		results.append(pool.apply_async(estimate_area, (begin, end)))
	pool.close()
	pool.join()
	area_section = sum(r.get() for r in results) # summing up partial areas 
	area_circle = 4 * area_section
	area_square = (2 * RADIUS) ** 2
	pi = 4.0 * area_circle / area_square
	t1 = datetime.now()
	error = abs(pi - math.pi)
	decimal_places = abs(math.trunc(math.log10(error)))
	print '{:.52f} \t estimated (correct decimal places: {:d})'.format(pi, decimal_places)
	print '{:.52f} \t math.pi'.format(math.pi)
	print '{:.52f} \t error'.format(error)
	print '{:>54s} \t elapsed time'.format((t1 - t0))


if __name__ == '__main__':
	main()

RADIUS = 10 ** 9
3.1415926535897646942885330645367503166198730468750000   estimated (correct decimal places: 13)
3.1415926535897931159979634685441851615905761718750000   math.pi
0.0000000000000284217094304040074348449707031250000000   error
                                        1:21:51.196000   elapsed time